Product to sum or difference forms and vice versa

Lesson#1
Product to sum or difference forms and vice versa
Exercise 10.4
Sum, Difference and Product of Sines and Cosines
Sum or diffrence form to Product form.
1) sinP+sinQ=2 sin⁡((P+Q)/2)cos((P−Q)/2)
2) sinP−sinQ=2 cos⁡((P+Q)/2)sin((P−Q)/2)
3) cosP+cosQ=2 cos⁡((P+Q)/2)cos((P−Q)/2)
4) cosP−cosQ=−2 sin⁡((P+Q)/2)sin((P−Q)/2)
Prove that:
1) 2 sinα cosβ=sin⁡(α+β)+sin⁡(α−β)
2) 2 cosα sinβ=sin⁡(α+β)−sin⁡(α−β)
3) 2 cosα cosβ=cos⁡(α+β)+cos⁡(α−β)
4) −2 sinα sinβ=cos⁡(α+β)−cos⁡(α−β)
Math.Ex.10.4, Part12-10.4
1) sinP+sinQ=2 sin⁡((P+Q)/2)cos((P−Q)/2)
1) sinP−sinQ=2 cos⁡((P+Q)/2)sin((P−Q)/2)
1) cosP+cosQ=2 cos⁡((P+Q)/2)cos((P−Q)/2)
1) cosP−cosQ=−2 sin⁡((P+Q)/2)sin((P−Q)/2)
Trigonometric Identities
Chapter No 10
Exercise No 10.4
Mathematics
part 1